Can a triangle have one obtuse angle and one right angle?

No a triangle can not have a right angle and an obtuse angle. The triangle would end up looking like a different shape completely.

No. A triangle's angle measures add up to 180 degrees. We are asked to fit a 90-degree angle (right angle) and an obtuse angle into the triangle. We know the value of the right angle (90 degrees) so we can subtract that from 180 to get 90 degrees (remaining to fit angles in). Since an obtuse angle is more than 90 degrees, and we only have 90 degrees left to use, this statement is not possible.

:)